Marcia - I did a "jagged" one with similar block configuration
http://www.quiltingboard.com/t-81428-1.htm
If you look at the second picture you will see I filled the sides with either whole, or half, plain black hexagons until there was a straight edge to add a border, which is also black.
Deal with the sides first to get your straight edges.
If you have one of the One Block Wonder books, it will show you in there how to deal with top and bottom points.
Basically before you join the seams between the horizontal strips of triangles, you cut a width of border fabric (if your triangles were cut at 3-3/4ins, you cut 3-1/2in width, cut it with about an inch longer than your border requirement width. Cut two (one for the top and one for the bottom of each row). Then at one end of each piece and matching the angle of the particular strip, cut a 60deg angle one end of the piece to match the joined strip of triangles. So in other words you will have the horizontal strip with the border already attached top and bottom. Then you join all your strips together, you can trim to exact width required.
Then you can add borders to the sides in the normal way.
Hope this helps.